/*	$OpenBSD: n_log1p.c,v 1.12 2016/09/12 04:39:47 guenther Exp $	*/
/*	$NetBSD: n_log1p.c,v 1.1 1995/10/10 23:37:00 ragge Exp $	*/
/*
 * Copyright (c) 1985, 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

/* LOG1P(x)
 * RETURN THE LOGARITHM OF 1+x
 * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 1/19/85;
 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.
 *
 * Required system supported functions:
 *	scalbn(x,n)
 *	copysign(x,y)
 *	logb(x)
 *	isfinite(x)
 *
 * Required kernel function:
 *	log__L(z)
 *
 * Method :
 *	1. Argument Reduction: find k and f such that
 *			1+x  = 2^k * (1+f),
 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *	2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
 *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
 *	   log(1+f) is computed by
 *
 *	     		log(1+f) = 2s + s*log__L(s*s)
 *	   where
 *		log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
 *
 *	   See log__L() for the values of the coefficients.
 *
 *	3. Finally,  log(1+x) = k*ln2 + log(1+f).
 *
 *	Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
 *		   n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
 *		   20 bits (for VAX D format), or the last 21 bits ( for IEEE
 *		   double) is 0. This ensures n*ln2hi is exactly representable.
 *		2. In step 1, f may not be representable. A correction term c
 *	 	   for f is computed. It follows that the correction term for
 *		   f - t (the leading term of log(1+f) in step 2) is c-c*x. We
 *		   add this correction term to n*ln2lo to attenuate the error.
 *
 *
 * Special cases:
 *	log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;
 *	log1p(INF) is +INF; log1p(-1) is -INF with signal;
 *	only log1p(0)=0 is exact for finite argument.
 *
 * Accuracy:
 *	log1p(x) returns the exact log(1+x) nearly rounded. In a test run
 *	with 1,536,000 random arguments on a VAX, the maximum observed
 *	error was .846 ulps (units in the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include <errno.h>
#include "math.h"
#include "mathimpl.h"

static const double ln2hi = 6.9314718055829871446E-1;
static const double ln2lo = 1.6465949582897081279E-12;
static const double sqrt2 = 1.4142135623730950622E0;

double
log1p(double x)
{
	static const double zero=0.0, negone= -1.0, one=1.0,
		      half=1.0/2.0, small=1.0E-20;   /* 1+small == 1 */
	double z,s,t,c;
	int k;

	if (isnan(x))
		return (x);

	if(isfinite(x)) {
	   if( x > negone ) {

	   /* argument reduction */
	      if(copysign(x,one)<small) return(x);
	      k=logb(one+x); z=scalbn(x,-k); t=scalbn(one,-k);
	      if(z+t >= sqrt2 )
		  { k += 1 ; z *= half; t *= half; }
	      t += negone; x = z + t;
	      c = (t-x)+z ;		/* correction term for x */

 	   /* compute log(1+x)  */
              s = x/(2+x); t = x*x*half;
	      c += (k*ln2lo-c*x);
	      z = c+s*(t+__log__L(s*s));
	      x += (z - t) ;

	      return(k*ln2hi+x);
	   }
	/* end of if (x > negone) */

	    else {
#if defined(__vax__)
		if ( x == negone )
		    return (infnan(-ERANGE));	/* -INF */
		else
		    return (infnan(EDOM));	/* NaN */
#else	/* defined(__vax__) */
		/* x = -1, return -INF with signal */
		if ( x == negone ) return( negone/zero );

		/* negative argument for log, return NaN with signal */
	        else return ( zero / zero );
#endif	/* defined(__vax__) */
	    }
	}
    /* end of if (isfinite(x)) */

    /* log(-INF) is NaN */
	else if(x<0)
	     return(zero/zero);

    /* log(+INF) is INF */
	else return(x);
}